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Simplifying (4v + -2)(9 + v) = 0 Reorder the terms: (-2 + 4v)(9 + v) = 0 Multiply (-2 + 4v) * (9 + v) (-2(9 + v) + 4v * (9 + v)) = 0 ((9 * -2 + v * -2) + 4v * (9 + v)) = 0 ((-18 + -2v) + 4v * (9 + v)) = 0 (-18 + -2v + (9 * 4v + v * 4v)) = 0 (-18 + -2v + (36v + 4v2)) = 0 Combine like terms: -2v + 36v = 34v (-18 + 34v + 4v2) = 0 Solving -18 + 34v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 17v + 2v2) = 0 Factor a trinomial. 2((-9 + -1v)(1 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve: Simplifying -9 + -1v = 0 Solving -9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1v = 0 + 9 -1v = 0 + 9 Combine like terms: 0 + 9 = 9 -1v = 9 Divide each side by '-1'. v = -9 Simplifying v = -9Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5Solution
v = {-9, 0.5}
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